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2011 Nov 24
1
CAPM-GARCH - Regression analysis with heteroskedasticity
...rns
and squared returns. Looks good - stylised facts seems to be covered.
Starting with GARCH:
I use a GARCH(1,1) but will use it as an infinite ARCH(1,1):
Let h be the variance. ?_1 and a0 the coefficents and r2 the squared
returns:
Infinitive ARCH Model:
h<-ao*sum(?_1^i)+a1*sum(?_1^(i-1)*r2_{t-i})
How I used it in R:
sumofbeta<- ?_1^rep(1:length(r2)) # Beta-Seq sum(?_1^i) for the sum of the
product
h<-a0*(1/1-?_1)+a1*(t(sumofbeta)%*%r2)
Now i have my variance:
DOING THE CAPM:
Applying a simple regression analysis
ri <- alpha+beta*rm+e
e ~ N(0,h)
h is following the GAR...